76629 ÷ 6 = 12771 R3
Alright, let's work through the division of 76629 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 2:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 16 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 6

Step 3:
6 goes into 46 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 127
Subtract 42 from 46 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 6

Step 4:
6 goes into 42 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 1277
Subtract 42 from 42 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 6

Step 5:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 12771
Subtract 6 from 9 to get 3.

The final result is 12771 with a remainder of 3.